Note: this is not my homework i was just doing this junior physics Olympiad paper as a practice. the link to question: https://www.scribd.com/document/244111815/SJPO-2013-Special-Round-pdf sorry could not get a soft copy anyways it is question 10 of the paper. what does the question mean by the proton grazes past the sphere and does it mean the proton continues moving from there onwards? and what is the approach to this problem is it conservation of energy and what the variable " l " got anything to do with the problem. while i understand that this problem can be solved with a calculus based approach please don't use one as the competition does not require the use of calculus thanks any help would be appreciated !!!!